Mean square error analysis of nonuniform subband adaptive filters for system modeling

Nonuniform filterbanks have recently been proposed for subband adaptive filters (SAFs). However, nonuniform SAFs have not yet been given a thorough performance analysis. This paper gives a comprehensive mean square error (MSE) analysis of system modeling, nonuniform (and, degeneratively, uniform) SAFs after convergence for a specified filterbank. Using the equivalent polyphase representation suggested by Ono et al., minimum MSE (MMSE) estimates for the individual subband errors are presented with respect to a given filterbank for finite length (FIR), infinite length causal (IIR), and infinite noncausal adaptive filters. Using these subband MMSE estimators, an MMSE estimator is derived for the overall fullband error. Finally, the derived MMSE estimators are verified by a numerical simulation. The intent of this paper is not to compare nonuniform and uniform SAF performance but merely to present a unified mathematical methodology to predict their MMSEs.

[1]  Dennis R. Morgan,et al.  A delayless subband adaptive filter architecture , 1995, IEEE Trans. Signal Process..

[2]  Clifford T. Mullis,et al.  A Newton-Raphson method for moving-average spectral factorization using the Euclid algorithm , 1990, IEEE Trans. Acoust. Speech Signal Process..

[3]  Tamal Bose,et al.  Channel equalization using an Euclidean direction search based adaptive algorithm , 1998, IEEE GLOBECOM 1998 (Cat. NO. 98CH36250).

[4]  Byeong Gi Lee,et al.  A design of nonuniform cosine modulated filter banks , 1995 .

[5]  B. Hofmann-Wellenhof,et al.  Introduction to spectral analysis , 1986 .

[6]  Martin Vetterli,et al.  Adaptive filtering in subbands with critical sampling: analysis, experiments, and application to acoustic echo cancellation , 1992, IEEE Trans. Signal Process..

[7]  S. Haykin,et al.  Adaptive Filter Theory , 1986 .

[8]  D. M. Etter,et al.  Subband adaptive filtering decimation constraints for oversampled nonuniform filterbanks , 2002 .

[9]  Hitoshi Kiya,et al.  An equivalent model for subband adaptive system and analysis of its performance , 1995 .

[10]  Truong Q. Nguyen,et al.  A simple design method for near-perfect-reconstruction nonuniform filter banks , 1997, IEEE Trans. Signal Process..

[11]  D. Garcia-Alis,et al.  Subband adaptive equalization of time-varying channels , 1999, Conference Record of the Thirty-Third Asilomar Conference on Signals, Systems, and Computers (Cat. No.CH37020).

[12]  Tamal Bose,et al.  Non-uniform filterbank bandwidth allocation for system modeling subband adaptive filters , 1999, 1999 IEEE International Conference on Acoustics, Speech, and Signal Processing. Proceedings. ICASSP99 (Cat. No.99CH36258).

[13]  John J. Shynk,et al.  Adaptive equalization using multirate filtering techniques , 1991, [1991] Conference Record of the Twenty-Fifth Asilomar Conference on Signals, Systems & Computers.

[14]  Truong Q. Nguyen.  Near-perfect-reconstruction pseudo-QMF banks , 1994, IEEE Trans. Signal Process..

[15]  Edward J. Wegman,et al.  Statistical Signal Processing , 1985 .

[16]  Mariane R. Petraglia,et al.  A new critically sampled non-uniform subband adaptive structure , 2001, 2001 IEEE International Conference on Acoustics, Speech, and Signal Processing. Proceedings (Cat. No.01CH37221).

[17]  Delores M. Etter,et al.  Subband adaptive filtering with time-varying nonuniform filter banks , 1997, 1997 IEEE International Conference on Acoustics, Speech, and Signal Processing.

[18]  Mariane R. Petraglia,et al.  New structures for adaptive filtering in subbands with critical sampling , 2000, IEEE Trans. Signal Process..

[19]  Hitoshi Kiya,et al.  Performance analysis of subband adaptive systems using an equivalent model , 1994, Proceedings of ICASSP '94. IEEE International Conference on Acoustics, Speech and Signal Processing.

[20]  P. P. Vaidyanathan,et al.  Effects of Multirate Systems on the Statistical Properties of Random Signals , 1993, IEEE Trans. Signal Process..

[21]  Delores M. Etter,et al.  Experimental results with increased bandwidth analysis filters in oversampled, subband acoustic echo cancelers , 1995, IEEE Signal Processing Letters.